For convexly curved lightweight building constructions, it is known to use the form of zonohedrons (U.S. Pat. No. 3,722,153 to Steve Baer, Mar. 27, 1973). However, the geometry described therein, with its vector star at the pentagonal dodecahedron and at the icosahedron as the fundamental polyhedron, is mostly unsuitable for use in the construction field. Although other vector stars are not expressly excluded, they are not shown, either.
Attempts to embody the constructions, which are called "zomes", in the 3,722,153 patent, in the form of bars in what in a static sense is genuine trusswork, involves monstrous node connections, which previously were surely used only for climbing scaffolds ("The Discovery of Space Frames with Fivefold Symmetry", in the book entitled Fivefold Symmetry, edited by Istvan Hargittai, Budapest, 1991, 1992, World Scientific Publishing, Singapore, pages 205 ff).
In the same book, the possibility of creating further geometric structures with an arbitrary vector star is discussed fundamentally by Haresh Lalvani in his article "Continuous Transformations of Non-Periodic Tilings and Space-Fillings", pages 97 ff. In the description in the article of the possible regular location of edge vectors from the center of an imaginary cube through points on a triangular quarter-segment of one side of a cube in FIG. 17, page 115, there is a failure to define a geometric structure that is not merely novel but also readily usable. His construction system (U.S. Pat. No. 4,723,382, Feb. 9, 1998) has only limited utility, and not merely in terms of the geometry of the system lines. The connection proposed therein is suitable for only very thin
Until now, connecting shallow, planar elements in three-dimensionally extended load-bearing surfaces has been achieved only with very slight plate thicknesses, which are unfavorable in terms of statics and heat protection. Thicker plates, however, have the disadvantage of becoming undesirably canted against one another. This situation is mentioned by Dave Mielke in his report on constructing a zome (The Dome Builder's Handbook, edited by John Prenis, Philadelphia, Pa., 1973/1985, page 74). Cutting mitered edges where the edges end and meet makes the corners uneven.
The New York artist Tony Robbins also proposes making three-dimensional supporting framework surfaces from plates. These structures are in at least two layers, however, because they must be put together from parallelepiped "cells" in the form of blocklike units which individually comprise six mitered plates of the same lozenge format ("Quasicrystal Architecture", in: IASS Copenhagen, 1991, Vol. 2, pages 45 ff; Engineering a New Architecture, New Haven and London, 1996), FIGS. 44, 45 and pages 81 ff).
The "Min-a-Max Building System" (Peter Pearce: Structure in Nature is a Strategy for Design, Cambridge, Massachusetts and London, 1978 and 1990, Page 199) was reduced to practice only in the form of a model construction system (U.S. Pat. No. 3,600,825: Synthesized Natural Geometric Structures). With its vector star oriented in the cube, it also makes it possible to produce zomes from packs of rhombic dodecahedra, but its disposition in horizontal projection is in triagonal-hexagonal symmetry, thus resulting in diagonal walls that are unfavorable to use. These are avoided by J. Francois Gabriel--again at the cost of space utilization ("Polyhedra: Skin and Structure" in IASS Working Group No. 15/IL Stuttgart (editors): Application of Structural Morphology, in the Proceedings of the Second International Seminar on Structural Morphology, Stuttgart, 1994).
Geometrically neat connections in three-dimensional trusswork with fillings, similar to traditional wood half-timbering, was already developed over 20 years ago by Walter Kuhn. Its use is restricted, however, to the conventional three-dimensional trusswork structures made up of cubes, tetrahedrons and octahedrons ("Geometrische Gitter und ihre Konkretisierung und Realisierung in Raumfachwerken" [Geometric Lattices and their Reduction to Practice and Realization in Three-Dimensional Trusswork Constructions], in: Second International Conference on Space Structures, organized by Department of Civil Engineering, University of Surrey, Great Britain, 1975).
Thus the use of complex space structures remains actually limited to educational or toy building sets. Examples of this are "Googolplex" made by Arlington-Hews in Vancouver, Canada (Allen W. Banboury, Investigating polygons and polyhedra with Googolplex, Vancouver and Philadelphia, 1988), or the "Zometool" made by Biocrystal, Inc. in Boulder, Colorado. (David Booth: "The New Zome Primer", in the aforementioned book edited by I. Hargittai, pages 221 ff).
With regard to the classification and effect of polyhedrons, publications by Helmut Emde (Darmstadt), Peter Pearce (Chatsworth, Calif.) and Ture Wester (Copenhagen) are available.